Multi-Objective Optimization Model for Renewable Energy Technologies under Uncertainty: A South African Case

This paper presents an original multi-objective optimization model for increasing the generation capacity of renewable technologies under stochastic power outages and load shedding. The model aims to minimize the total costs of capital, and operations and maintenance (O&M), while maximizing the number of total annual jobs created in the manufacturing, installation, and operation phases of the renewable energy sources (RES). The model focuses on wind, solar photovoltaic (PV), and concentrated solar power (CSP) technologies predominantly used in South Africa. Lithium-ion batteries are used as a storage system to stockpile energy for the anticipation of load shedding. Two intervention methods, Expected Value Approach (EVA) and Scenario Chance Constrained Programming (SCCP), are applied to derive the deterministic equivalents of the stochastic constraints. A preemptive optimization approach is used to reduce the multi-objective model to single-objective solutions. The coefficient of variation is then used to compare the variation of the renewable generation from the two methods to the profile of the historical generation. The SCCP has a lower percentage error of variation than the EVA, thus validating its application when precision is critical. A sensitivity analysis is performed by varying the minimum required contribution parameter, which shows an upward trend in the total costs and annual jobs mainly influenced by increasing the capacity of CSP and PV respectively. The study uses a novel model to estimate renewable generation required to offset generation deficit, thus illustrating that increasing the nominal capacities of the RES in South Africa can mitigate the crisis of power outages.